Black Jack Odds Calculator

Playing this game for years by using basic strategy, at a certain moment I felt that it was something more that could be done. After a while, with an add of my personal strategy and intuition, I managed to earn some money, but I felt that earnings could be higher with the deepening of certain aspects of the game. I am quite good in programming, I am talking about Visual Basic, and even math is the subject I was good in it, so I decided to create a software that will give me more information about the course of the hand, especially when I have more than two cards (with two cards also the basic strategy is enough). In such a way was born BJC, Black Jack Calculator which you can download from this page and use for free.

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Free Download

Extremely easy to use, calculator is kept open along with the application for Black Jack, by selecting the cards you are dealt during the game and in that way you get information on the odds of the dealer and the player. The program is as easy to install. It's necessery to download BJC.ZIP file (link below the image), unzip and save it into any directory (I recommend the desktop, so it can always be handy) and the software is ready for action. BJC does not require any installation, doesn't records anything in the Windows registry, does not create files on your hard disk, not connecting to the Internet during work, there is no need to use any license and is free to be copied.

Clicc here to dowload free Black Jack Odds Calculator
(Size of the file: 15 kB)

The software is very intuitive and simple to use, but in any case on this page we will present short instructions for use and explanations of the correct interpretation of the results provided. BJC doesn't give advice how to play but gives you information about the odds that could be useful to take the right decision during he game.

Free black jack odds calculator to download

Software Interface

BJC's window is divided into four horizontal sections: the first two are data for the dealer and the player, in the third section are presented the conditions with which the application operates and two buttons to start a new hand and calculate odds. In the last part, at the bottom of the window, there are two Internet links that are taking you to this site and right on this page, just in case you need something to remind, or clear some details.

Black jack software interface

The Dealer and the Player data

The information for the processing are the cards of the dealer and those of the player. In order to give cards to the dealer and to the player it's enough to click on the card symbols in the relevant fields. Selected cards are shown in blue below that field and the program automatically displays the sum behind the big letter S, also marked in blue.

As soon the dealer receive at least one card and the player receive two cards, BJC automatically calculates the odds for both entities and writes them in the relative field on the right side: the probability of the dealer and the probability of the player. If you are making a mistake during the input of cards, you need to click Cancel buttom, to erase cards and enter them again.

In the field Player is present an additional parameter which can be changed as you like: Stop at. This information is necessary that the program would know where to stop the game and calculate the probabilities related to that sum. The initial value is 17, same as for the dealer.

Basic bottons

In the third horizontal field, along with a presentation of basic, unchangeable parameters used by the program, are present two buttons. The button "new hand" cancels registered cards to start new hand, while button "calculate", makes that BJC calculates odds in relation with the actual cards. Since software automatically elaborates the values in the process of card inputting, this key seems superfluous. In fact, it is necessary to re-calculate data, that means press this button, only if the value of the parameter "stop at" is changed by user, keeping cards that have already been registered.

Results

In function of the selected cards, BJC performs quite complex combinatorial operations and gives to user information about the odds of various possible outcomes of the game. First of all, gives two sets of output: a percentage related to the first card, and the final one, which takes into account all the possible combinations that can be formed with the remaining cards in the deck. A data type that is given to the player and the dealer is somewhat different because the player is the one who always gets cards first. To improve the visibility of the results, rows that have the zero percentage are omitted. For the dealer are printed 4 percentages, as follows:
  • Probability of the winning, the dealer achieved a sum bigger than the player;
  • Probability for the tie, the dealer reaches the same amount as a player;
  • Pobability that the dealer loses, that means the dealer's sum is less than the player's sum;
  • Probability that dealer busts, by going over 21.

For the player, considering he plays first and has no reference points, we have only two percentages:

  • Probability to reach or to exceed, but not to bust, the sum of the cards defined with the parameter "stop at";
  • Probability to bust, that means go over 21.

Why this difference between the type of data that BJC gives? Since the dealer has only one card, there is no way to predict its final results, and therefore it's not possible to access percentages of players for win, tie and loss, in fact, this three percentages are contained in the value "stop at". Caution regarding the odds for the win and the tie of the dealer. The same do not have much meaning when a player has a very low sum of (let's say that the first two cards are 2 and 4), far from the final results. These values become more fair and make sense only when the player reaches the desired result.

Interpretation of the results

How to interpret the results and apply them to the game is the most important question for the player that use Black Jack Calculator. At the end of the story, we are not really interested on the odds, our aim is to win and beat the dealer and the probabilities are only an instrument to reach our main purpose. The most important comparison is the one between the probabilities to bust, ours and the dealer's. The fact is that our most problematic positions are the one that give us the sum between 12 and 16

The first reason is that with any card that has a value of 10 we fall, on the other hand it seems that we are too week to win, because the dealer can not stop before it reaches 16. Looking at the problem in this way, if our probability to bust is bigger than the probability of the dealer to win, we stand, we don't ask for the card. Otherwise, when the probability of the dealer for the win is bigger from our probability to bust, we are taking another card. Also the other probabilities have a value and can be taken in consideration before the final decision is taken to continue the game.

An example

For those of you that are curios, we will develop in detail an example to better understand the mode of BJC's work. For example, the dealer has 7 and the player has 10 and 6. In the table are the results of this example, made by BJC.

Probabilities of Dealer
First CardAll Combinations
Win38,78% Win68,18%
Tie8,16% Tie13,25%
   Bust18,57%

Probabilities of Player
First CardAll Combinations
>= 1740,82% >= 1740,82%
Bust59,18% Bust59,18%

With the first card the dealer wins with a probability of 38.8% (this is one of the values manually calculated to confirm the validity of results) and has the 8.2% possibilities to achieve a parity (card 9). The dealer can not loose because it must reach a minimum of 16, which is the sum of the players and with the first card can not fall so these two items are not displayed as output. Considering all possible combinations, that means with 2, 3 or more cards which dealer can take, we have the values entered in the above table under the column "all combinations".

On the other hand, the player has the same probability for the first card and all the combinations, this will be discussed in detail and shown a bit below in the text. Player's probability to bust is 59.2 %, lower than the probability of dealer's winning (68,2% for all the combination, which are always taken in consideration) and therefore the player should take a card, according to the indications shown in the table of basic strategy.

Speaking of all possible combinations, BJC, to be able to give the final result, generate all of them and control the same outcome. Depending on the drawn cards, sometimes it's necessary to create and compare thousands of combinations. Here are just some of them, in order how they are calculated by software, because they are too many to be listed on this page, generated for the dealer for this example (in the following listing A means As):

7 | A / SUM= 18  Win
7 | 2  A / SUM= 20  Win
7 | 2  2  A  A  A  A   2/SUM= 17 Win
7 | 2  2  A  A  A  A   3/SUM= 18 Win
7 | 2  2  A  A  A  A   4/SUM= 19 Win
7 | 2  2  A  A  A  A   5/SUM= 20 Win
7 | 2  2  A  A  A  A   6/SUM= 21 Win
7 | 2  2  A  A  A  A   7/SUM= 22 Bust
7 | 2  2  A  A  A  A   8/SUM= 23 Bust
7 | 2  2  A  A  A  A   9/SUM= 24 Bust
7 | 2  2  A  A  A  A  10/SUM= 25 Bust
7 | 2  2  A  A  A  2/SUM= 16 Tie

. . .

7 | 8   A / SUM= 16  Tie
7 | 8   2 / SUM= 17  Win
7 | 8   3 / SUM= 18  Win
7 | 8   4 / SUM= 19  Win
7 | 8   5 / SUM= 20  Win
7 | 8   6 / SUM= 21  Win
7 | 8   7 / SUM= 22  Bust
7 | 8   8 / SUM= 23  Bust
7 | 8   9 / SUM= 24  Bust
7 | 8  10 / SUM= 25  Bust

Regarding the combinations of the player, always talking about the previous example, they are much less, to be precise exactly 10, as the various values that the cards have. In fact, for the player exist only combination with one card, because with it goes over the limit "Stop at" and automatically stops, or busts. Saw that the number of combinations is small, below are listed all.

10+6 |  A / SUM = 17  => Stop
10+6 |  2 / SUM = 18  => Stop
10+6 |  3 / SUM = 19  => Stop
10+6 |  4 / SUM = 20  => Stop
10+6 |  5 / SUM = 21  => Stop
10+6 |  6 / SUM = 22  Bust
10+6 |  7 / SUM = 23  Bust
10+6 |  8 / SUM = 24  Bust
10+6 |  9 / SUM = 25  Bust
10+6 | 10 / SUM = 26  Bust
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